Séminaire Lotharingien de Combinatoire, B44c (2000), 3 pp.

Herbert S. Wilf

Identically Distributed Pairs of Partition Statistics

Abstract. We show that many theorems which assert that two kinds of partitions of the same integer n are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics X and Y that have identical distribution functions. The method is an extension of the principle of sieve-equivalence, and it yields simple criteria under which we can infer this identity of distribution functions.

Received: April 25, 2000; Accepted: May 19, 2000.

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